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The perimeter of a triangle is 54 m and its sides are in the ratio of 5 : 6 : 7. The area of the triangleis
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- 18 m²
- 54√6 m²
- 27√2 m²
- 25 m²
- 18 m²
Correct Option: B
Using Rule 1,
Ratio of the lengths of sides = 5 : 6 : 7
Sum of ratios = 5 + 6 + 7 = 18
| ⇒ Sides ⇒ | × 54 = 15 metre | |
| 18 |
| × 54 = 18 metre | ||
| 18 |
| × 54 = 21 metre | ||
| 18 |
| Semi-perimeter (s) = | = | = 27 | ||
| 2 | 2 |
∴ Area of triangle = √s(s - a)(s - b)(s - c)
= √27(27 - 15)(27 - 18)(27 - 21)
= √27 × 12 × 9 7times; 6
= √3 × 3 × 3 × 2 × 2 × 3 × 3 × 3 × 2 × 3 = 3 × 3 × 3 × 2 6 =
= 3 × 3 × 3 × 2√6
= 54√6 sq.metre
